(2x-3)(5-6x)=3x(4x-1)

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Solution for (2x-3)(5-6x)=3x(4x-1) equation:


Simplifying
(2x + -3)(5 + -6x) = 3x(4x + -1)

Reorder the terms:
(-3 + 2x)(5 + -6x) = 3x(4x + -1)

Multiply (-3 + 2x) * (5 + -6x)
(-3(5 + -6x) + 2x * (5 + -6x)) = 3x(4x + -1)
((5 * -3 + -6x * -3) + 2x * (5 + -6x)) = 3x(4x + -1)
((-15 + 18x) + 2x * (5 + -6x)) = 3x(4x + -1)
(-15 + 18x + (5 * 2x + -6x * 2x)) = 3x(4x + -1)
(-15 + 18x + (10x + -12x2)) = 3x(4x + -1)

Combine like terms: 18x + 10x = 28x
(-15 + 28x + -12x2) = 3x(4x + -1)

Reorder the terms:
-15 + 28x + -12x2 = 3x(-1 + 4x)
-15 + 28x + -12x2 = (-1 * 3x + 4x * 3x)
-15 + 28x + -12x2 = (-3x + 12x2)

Solving
-15 + 28x + -12x2 = -3x + 12x2

Solving for variable 'x'.

Reorder the terms:
-15 + 28x + 3x + -12x2 + -12x2 = -3x + 12x2 + 3x + -12x2

Combine like terms: 28x + 3x = 31x
-15 + 31x + -12x2 + -12x2 = -3x + 12x2 + 3x + -12x2

Combine like terms: -12x2 + -12x2 = -24x2
-15 + 31x + -24x2 = -3x + 12x2 + 3x + -12x2

Reorder the terms:
-15 + 31x + -24x2 = -3x + 3x + 12x2 + -12x2

Combine like terms: -3x + 3x = 0
-15 + 31x + -24x2 = 0 + 12x2 + -12x2
-15 + 31x + -24x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
-15 + 31x + -24x2 = 0

Begin completing the square.  Divide all terms by
-24 the coefficient of the squared term: 

Divide each side by '-24'.
0.625 + -1.291666667x + x2 = 0

Move the constant term to the right:

Add '-0.625' to each side of the equation.
0.625 + -1.291666667x + -0.625 + x2 = 0 + -0.625

Reorder the terms:
0.625 + -0.625 + -1.291666667x + x2 = 0 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + -1.291666667x + x2 = 0 + -0.625
-1.291666667x + x2 = 0 + -0.625

Combine like terms: 0 + -0.625 = -0.625
-1.291666667x + x2 = -0.625

The x term is -1.291666667x.  Take half its coefficient (-0.6458333335).
Square it (0.4171006947) and add it to both sides.

Add '0.4171006947' to each side of the equation.
-1.291666667x + 0.4171006947 + x2 = -0.625 + 0.4171006947

Reorder the terms:
0.4171006947 + -1.291666667x + x2 = -0.625 + 0.4171006947

Combine like terms: -0.625 + 0.4171006947 = -0.2078993053
0.4171006947 + -1.291666667x + x2 = -0.2078993053

Factor a perfect square on the left side:
(x + -0.6458333335)(x + -0.6458333335) = -0.2078993053

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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